$A$ Gaussian surface of radius $R$ encloses a charge $Q$. If the radius is doubled,the outward electric flux will...

The figure shows four charges $q_1, q_2, q_3$ and $q_4$ fixed in space. The total flux of the electric field through a closed surface $S$,due to all charges $q_1, q_2, q_3$ and $q_4$ is:

Choose the incorrect statement:
$(a)$ The electric lines of force entering into a Gaussian surface provide negative flux.
$(b)$ $A$ charge '$q$' is placed at the centre of a cube. The flux through all the faces will be the same.
$(c)$ In a uniform electric field,the net flux through a closed Gaussian surface containing no net charge is zero.
$(d)$ When the electric field is parallel to a Gaussian surface,it provides a finite non-zero flux.
Choose the most appropriate answer from the options given below:

Careful measurement of the electric field at the surface of a black box indicates that the net outward flux through the surface of the box is $8.0 \times 10^{3} \; N m^{2} / C$.
$(a)$ What is the net charge inside the box?
$(b)$ If the net outward flux through the surface of the box were zero,could you conclude that there were no charges inside the box? Why or why not?

If some charge is given to a solid metallic sphere,the field inside remains zero and by Gauss's law all the charge resides on the surface. Now,suppose that Coulomb's force between two charges varies as $1 / r^{3}$. Then,for a charged solid metallic sphere

The flux of the electric field $\overrightarrow{E} = 24 \hat{i} + 30 \hat{j} + 28 \hat{k} \text{ NC}^{-1}$ through an area of $20 \text{ m}^2$ on the $yz$ plane is